Calculus education research on integration is coalescing around the theme that teaching integration based on quantitative reasoning is crucial for robust understanding of and usage of integrals. This paper contributes to this International Journal for Research in Undergraduate Education special issue on the teaching and learning of definite…

Informal Australian discussion suggests that calculators are still widely regarded as devices for calculation, consistent with their naming, and are rarely recognised as potentially helpful to support students learning mathematics. In this paper, Barry Kissane explores some of the ways in which modern calculators might support students learning…

The results of this study revealed students' solution strategies progressed from inefficient strategies e.g., counting on fingers to more efficient strategies with mathematical connections. These findings should enable educators to gain more insight to use Number Talks to help student develop computational fluency with numbers.

Mathematics is pivotal in the contemporary technology-driven world. However, poor mathematical performance continues to be a concern in many countries. Guided by Mathematics in a Cultural Context (MCC) framework, this article investigates the similarities, differences, and potential reasons behind early numeracy achievement in South Africa and…

The OECD Future of Education and Skills 2030 report on mathematics curriculum presents first-of-its-kind comparative data on how countries are adapting curricula to meet the demands of the 21st century. The project's unique data illustrate a 25-year evolution of mathematics curricula in various countries, looking at content coverage and the…

Issues within college algebra are well-documented. Over the past two decades, reform has brought about significant modifications in the course, yet to date there has been no synthesis of the efficacy of these efforts. This paper situates college algebra within a historical context, and synthesizes research on reform. I argue that, notwithstanding…

This proposal explores relationships between young children's unit development/coordination and young children's subitizing. In particular, this theoretical commentary considers students' degrees of abstraction, students' development of actions on units, and students' operations with units when subitizing. As a result of this commentary, this…

In this paper we present statistical analyses of three textbooks used by Swedish teachers to support year one children's learning of mathematics. One, Eldorado, is authored by Swedish teachers, another, Favorit, is a Swedish adaptation of a popular Finnish series and the third, Singma, is a Swedish adaptation of a Singapore series. Data were coded…

Increasingly, digital technologies are being utilised to provide opportunities for teacher professional learning (PL) in fully online, blended and face-to-face environments. Videos have been used extensively across the three modes of delivery but there appears little research on the conceptual framing underpinning their development. This article…

We share a subset of the 41 underlying strategies that comprise five ways of reasoning about integer addition and subtraction: formal, order-based, analogy-based, computational, and emergent. The examples of the strategies are designed to provide clear comparisons and contrasts to support both teachers and researchers in understanding specific…

Many resources have been created with the aim of helping children and adults overcome difficulties with mathematics and to develop or improve their numeracy. However, these are only used once the individual has decided to act -- to do something to improve their mathematics and numeracy. Unfortunately, someone who knows that they need to improve…

This paper analyzes factors that affect the numeracy skills of secondary school students from mountainous and ethnic minority regions in Vietnam from the perspective of the students to create suitable strategies for teachers, parents, and the government to enhance their numeracy skills. Data from 755 students in 8 secondary schools in 8 provinces…

The three target articles presented in this special issue converged on an emerging theme: the importance of spatial proportional reasoning. They suggest that the ability to map between symbolic fractions (like 1/5) and nonsymbolic, spatial representations of their sizes or "magnitudes" may be especially important for building robust…

The diversity of vulnerability conditions, that have prevented children and adolescents from exercising their right to school education, also produces a diversity of cultural references of the public that comes to Basic Education programs for Youth and Adults in developing countries. This diversity often forges appropriation processes of numeracy…

In the 2012 PIAAC Survey of Adult Skills of 23 industrialised countries, the UK (England & NI) scored below average on adult numeracy. Several recommendations focus on the need for (some) individuals in the population to undergo training. Yet, even in "high-performing countries" like the Netherlands, many adults (1.5M) score at or…